A tooth sharpener is a small hand-held device with a cylindrical grinder at one end, used by Ferengi to sharpen their teeth. The grinder rotates at high speeds and is applied to the edges of a tooth in order to sharpen it. Although Klingons also have relatively sharp teeth, Worf had never seen one before.
Rom owned a latinum-plated tooth sharpener as a child and the device held a strong sentimental value for him. (DS9: "Family Business") His son, Nog, held a similar attachment to his own tooth-sharpener and it was among the personal items that he auctioned off prior to his departure for Starfleet Academy where it was purchased by Worf. (DS9: "Little Green Men")